Find y₂ and y₃ for the following table, given that x varies directly from y.

x	2	3	4
y	8	y2	y3

In the case of direct proportions both the quantities change in the same direction and same proportion.

So, $\frac{{\mathrm{x}}_1}{{\mathrm{y}}_1}=\frac{{\mathrm{x}}_2}{{\mathrm{y}}_2}=\frac{{\mathrm{x}}_3}{{\mathrm{y}}_3}$

=> $\frac{{\mathrm{x}}_1}{{\mathrm{y}}_1}=\frac{{\mathrm{x}}_2}{{\mathrm{y}}_2}$

=> $\frac{2}{8}=\frac{3}{{\mathrm{y}}_2}$

=> ${\mathrm{y}}_2=\frac{24}{2}$

=> ${\mathrm{y}}_2=12$

Now, $\frac{{\mathrm{x}}_2}{{\mathrm{y}}_2}=\frac{{\mathrm{x}}_3}{{\mathrm{y}}_3}$

=> $\frac{3}{12}=\frac{4}{{\mathrm{y}}_3}$

=> ${\mathrm{y}}_3=\frac{48}{3}$

=> ${\mathrm{y}}_3=16$

Hence, ${\mathrm{y}}_2=12 \mathrm{and} {\mathrm{y}}_3=16$